SOLUTION: I can not figure out the following proportional question: In the figure, {{{AB/BC = AD/DE}}}. Use proportions to complete the following unknowns: AB=? BC=? AD=12 DE=? AC=

Algebra ->  Triangles -> SOLUTION: I can not figure out the following proportional question: In the figure, {{{AB/BC = AD/DE}}}. Use proportions to complete the following unknowns: AB=? BC=? AD=12 DE=? AC=      Log On


   

Question 405787: I can not figure out the following proportional question:
In the figure, AB%2FBC+=+AD%2FDE. Use proportions to complete the following unknowns:
AB=?
BC=?
AD=12
DE=?
AC=16
AE=20
The book says that AB=9.6, BC=6.4 and DE=8 but I am not sure how. Can someone please explain it.
Thanks.
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Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
DE = 8 because AE = 20, AD = 12, and DE = AE - AD.

Also, we have AB%2FBC+=+AD%2FDE, so AB%2FBC+=+12%2F8+=+3%2F2 and it follows that 3BC+=+2AB. AC = 16, so AB + BC = 16. Letting BC = 2x and AB = 3x, we have

5x = 16 --> x = 16/5, so BC = 32/5 = 6.4 and AB = 48/5 = 9.6.